• Advances in Computational Design
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• v.3 no.2
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• pp.165-190
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• 2018

In this article, the static behavior of non-prismatic sandwich beams composed of functionally graded (FG) materials is investigated for the first time. Two types of beams in which the variation of elastic modulus follows a power-law form are studied. The principle of minimum total potential energy is applied along with the Ritz method to derive and solve the governing equations. Considering conventional boundary conditions, Chebyshev polynomials of the first kind are used as auxiliary shape functions. The formulation is developed within the framework of well-known Timoshenko and Reddy beam theories (TBT, RBT). Since the beams are simultaneously tapered and functionally graded, bending and shear stress pushover curves are presented to get a profound insight into the variation of stresses along the beam. The proposed formulations and solution scheme are verified through benchmark problems. In this context, excellent agreement is observed. Numerical results are included considering beams with various cross sectional types to inspect the effects of taper ratio and gradient index on deflections and stresses. It is observed that the boundary conditions, taper ratio, gradient index value and core to the thickness ratio significantly influence the stress and deflection responses.

• Structural Engineering and Mechanics
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• v.59 no.1
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• pp.153-186
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• 2016

This paper addresses temperature-dependent nonlinear vibration and instability of embedded functionally graded (FG) pipes conveying viscous fluid-nanoparticle mixture. The surrounding elastic medium is modeled by temperature-dependent orthotropic Pasternak medium. Reddy third-order shear deformation theory (RSDT) of cylindrical shells are developed using the strain-displacement relations of Donnell theory. The well known Navier-Stokes equation is used for obtaining the applied force of fluid to pipe. Based on energy method and Hamilton's principal, the governing equations are derived. Generalized differential quadrature method (GDQM) is applied for obtaining the frequency and critical fluid velocity of system. The effects of different parameters such as mode numbers, nonlinearity, fluid velocity, volume percent of nanoparticle in fluid, gradient index, elastic medium, boundary condition and temperature gradient are discussed. Numerical results indicate that with increasing the stiffness of elastic medium and decreasing volume percent of nanoparticle in fluid, the frequency and critical fluid velocity increase. The presented results indicate that the material in-homogeneity has a significant influence on the vibration and instability behaviors of the FG pipes and should therefore be considered in its optimum design. In addition, fluid velocity leads to divergence and flutter instabilities.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.11
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• pp.973-981
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• 2013

The main role of an acoustic diffuser is to diffuse reflected sound field spatially. Since the pioneering work of Schroeder, there have been investigations to improve its performance by using shape/sizing optimization methods. In this paper, a gradient-based topology optimization algorithm is newly presented to find the optimal distribution of reflecting materials for maximizing diffuser performance. Time-harmonic acoustic analysis in a two-dimensional acoustic domain is carried out where the domain is discretized by finite elements. Perfectly matched layers are placed to surround the domain to simulate non-reflecting boundary conditions. Design variables are assigned to each element of which material properties are interpolated between those of air and those of a rigid body. An approach to extract the reflected field from the total acoustic field is employed. To validate the effectiveness of the proposed method, design problems are solved at different frequencies. The performance of the optimized diffusers obtained by the proposed method is compared against that of the conventional Schroeder diffusers.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.53-73
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• 2013

Prediction of prestressed concrete girder integral abutment bridge (IAB) load effect requires understanding of the inherent uncertainties as it relates to thermal loading, time-dependent effects, bridge material properties and soil properties. In addition, complex inelastic and hysteretic behavior must be considered over an extended, 75-year bridge life. The present study establishes IAB displacement and internal force statistics based on available material property and soil property statistical models and Monte Carlo simulations. Numerical models within the simulation were developed to evaluate the 75-year bridge displacements and internal forces based on 2D numerical models that were calibrated against four field monitored IABs. The considered input uncertainties include both resistance and load variables. Material variables are: (1) concrete elastic modulus; (2) backfill stiffness; and (3) lateral pile soil stiffness. Thermal, time dependent, and soil loading variables are: (1) superstructure temperature fluctuation; (2) superstructure concrete thermal expansion coefficient; (3) superstructure temperature gradient; (4) concrete creep and shrinkage; (5) bridge construction timeline; and (6) backfill pressure on backwall and abutment. IAB displacement and internal force statistics were established for: (1) bridge axial force; (2) bridge bending moment; (3) pile lateral force; (4) pile moment; (5) pile head/abutment displacement; (6) compressive stress at the top fiber at the mid-span of the exterior span; and (7) tensile stress at the bottom fiber at the mid-span of the exterior span. These established IAB displacement and internal force statistics provide a basis for future reliability-based design criteria development.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2002.10a
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• pp.100-105
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• 2002

This paper predicts the material properties of spatially reinforced composites (SRC) and analyzes the thermo-elastic behavior of a kick motor nozzle manufactured from that material. To find the appropriate SRC structure for the nozzle throat that satisfies given design conditions, the equivalent material properties of the SRC are predicted using the superposition method for those of rod and matrix. Studied are the elastic behavior, temperature distribution, and thermo-elastic behavior of a kick motor nozzle composed of carbon/carbon SRC as a throat part. The elastic deformation of the nozzle composed of 3D carbon/carbon SRC shows asymmetry in a circumferential direction. However, 4D carbon/carbon SRC nozzle shows uniform deformation in the circumferential direction. Stress concentration in connecting parts of the kick motor nozzle is ultimately high due to the high temperature gradient in each connecting part. The thermo-elastic deformations of both the 3D and the 4D SRC nozzles are uniform in the circumferential direction due to the isotropy of CTE of each SRC. The deformation of the 3D SRC nozzle is a slightly smaller than that of the 4D SRC nozzle in the nozzle throat, which is favorably effective on rocket thrust. The circumferential stress is the most critical component of the kick motor nozzle. The 4D SRC nozzle having 1,1,1,1.7 diameters in each direction has the smallest circumferential stress among several SRC nozzles.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1235-1242
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• 2006

Viscoelastic damping materials are widely used to reduce noise and vibration because of its low cost and easy implementation, for examples, on the body structure of passenger cars, air planes, electric appliances and ships. To design the damped structures, the material property such as elastic modulus and loss factor is essential information. The four-parameter fractional derivative model well describes the nonlinear dynamic characteristics of the viscoelastic damping materials with respect to both frequency and temperature with fewer parameters than conventional spring-dashpot models. However the identification procedure of the four-parameter is very time-consuming one. An efficient identification procedure of the four-parameters is proposed by using an FE model and a gradient-based numerical search algorithm. The identification procedure goes two sequential steps to make measured FRFs coincident with simulated FRFs: the first one is a peak alignment step and the second one is an amplitude adjustment. A numerical example shows that the proposed method is efficient and robust in identifying the viscoelastic material parameters of fractional derivative model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.1
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• pp.82-87
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• 1987

In this study a method of shape optimization is applied to two dimensional heat transfer system. For this the optimization problem is defined in a functional form including cost, constraints and the system governing equation. Then the material derivative concept in continuum mechanics and the adjoint variable method are employed for the shape design sensitivity analysis. With the sensitivity analysis results, an optimum is sought with the gradient projection optimization algorithm. The two dimensional isoparametric finite elements are used for accurate analysis and sensitivity calculations. The above method is employed to find the boundary shape to achieve a desired temperature distribution along a segment of the boundary subject to the maximum area constraint.

• Smart Structures and Systems
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• v.19 no.2
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• pp.115-126
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• 2017

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.30 no.12
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• pp.776-781
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• 2017

In this study, we investigated the effect of electrode pattern design on the thermal shock resistance and temperature uniformity of a ceramic heater. A cordierite substrate with a low thermal expansion coefficient was fabricated by tape casting, and a tungsten electrode was printed and used as a heating element. The temperature distribution of the ceramic heater was calculated by a finite-element method (FEM) by considering various electrode patterns, and the tensile stress distribution due to the thermal stress was calculated. In the electrode pattern with a single-line width, the central part of the ceramic heater was heated to the maximum temperature, and the position of the ceramic heater having a double-line width was changed to the maximum temperature, depending on the position of the minimum line width pattern. The highest tensile stress was found along the edges of the ceramic heater. The temperature gradient at the edge determined the tensile stress intensity. The smallest tensile stress was observed for electrode pattern D, which was expected to be advantageous in resisting thermal shock failures in ceramic heaters.

• Smart Structures and Systems
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• v.18 no.5
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• pp.1029-1062
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• 2016

In this research, the nonlinear free vibration analysis of boron-nitride micro ribbon (BNMR) on the Pasternak elastic foundation under electrical, mechanical and thermal loadings using modified strain gradient theory (MSGT) is studied. Employing the von $K{\acute{a}}rm{\acute{a}}n$ nonlinear geometry theory, the nonlinear equations of motion for the graphene micro ribbon (GMR) using Euler-Bernoulli beam model with considering attached mass and size effects based on Hamilton's principle is obtained. These equations are converted into the nonlinear ordinary differential equations by elimination of the time variable using Kantorovich time-averaging method. To determine nonlinear frequency of GMR under various boundary conditions, and considering mass effect, differential quadrature element method (DQEM) is used. Based on modified strain MSGT, the results of the current model are compared with the obtained results by classical and modified couple stress theories (CT and MCST). Furthermore, the effect of various parameters such as material length scale parameter, attached mass, temperature change, piezoelectric coefficient, two parameters of elastic foundations on the natural frequencies of BNMR is investigated. The results show that for all boundary conditions, by increasing the mass intensity in a fixed position, the linear and nonlinear natural frequency of the GMR reduces. In addition, with increasing of material length scale parameter, the frequency ratio decreases. This results can be used to design and control nano/micro devices and nano electronics to avoid resonance phenomenon.